77 lines
3.1 KiB
Markdown
77 lines
3.1 KiB
Markdown
---
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tags:
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- binary
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- computer-architecture
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---
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# Why computers use binary
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## Now we know how binary works, how does it relate to computing?
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The reason is straight forward: it is the simplest way on the level of pure
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engineering of representing numerical and logical values; both of which are the
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basic foundations of programming. An electronic circuit or transistor only needs
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to represent two states: on (1) and off (0) which corresponds to the switch on
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an electrical circuit. A single circuit representing the binary values of 1 and
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0:
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It would be much more complicated to have to represent ten different states
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under the decimal number system, although denary computers do exist.
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If we want more digits, we just need to add in more circuits, and we can
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represent as large a binary number as we need. We just need one switch for every
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digit we want to represent. The switches used in modern computers are so cheap
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and so small that billions can be fitted on a single circuit board.
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When we use the term 'switch' we actually mean the transistor components of a
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circuit. We don't need to know the physical details at this level but we can say
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that a transistor turns a current on and off. They can also be used to amplify
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the current.
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On the level of electrical engineering and in the subsequent examples using a
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light bulb and a simple circuit, the switch being OFF corresponds to the light
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being ON, this is because the switch breaks the current. So when it is unbroken,
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the current passes to the bulb. This also means that 1 corresponds to the switch
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being OFF and 0 corresponds to the switch being ON which can be confusing at
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first.
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## From circuits to programs
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The following breaks down how we get from the binary number system to electrical
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circuits to computer programs:
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1. ”Data”= a piece or pieces of **information**
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1. In computing all data is represented in **binary form:**
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2.1. ”Binary” means that the value of a piece of data is exclusively one
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thing or another
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2.2. The values in binary code are exclusively 1 and 0 (either a piece of
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data is a 1 or it is a 0, it can never be both). Binary can also be expressed
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in logical terms where 1 is equal to `true` and 0 is equal to `false`
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1. The smallest piece of data is a **bit**
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1. We apply the binary number system to bits
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1. Thus by 1-4, **a bit is either 1 or 0**
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1. Binary form bears an isomorphic relation to switches on electrical circuits
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(the hardware of computers). Thus binary code can be _mapped onto circuits_.
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- Circuits are controlled by switches
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- A switch is a binary function: it is either on or off ”On/off”
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corresponding to 1/0.
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- In this way, switches control the flow of electric current
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1. Thus by the above, hardware (which is a physical structure made up of
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electric circuits) is **readily programmable in binary terms**
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1. Restatement of 6: in order for hardware to be programmed the program must
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provide the hardware with something that it can actually perform. The program
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must be formulated in binary code.
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